In mathematics, a representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to another (abstract...

The Riesz representation theorem, sometimes called the Riesz–Fréchet representation theorem after Frigyes Riesz and Maurice René Fréchet, establishes...

In the mathematical discipline of group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup...

similarly named results, see Birkhoff's theorem (disambiguation). In mathematics, Birkhoff's representation theorem for distributive lattices states that...

an integrable function. In the latter case, the Gelfand–Naimark representation theorem is one avenue in the development of spectral theory for normal operators...

In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some latent variable. An epistemic...

analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous function...

In probability theory, the martingale representation theorem states that a random variable with finite variance that is measurable with respect to the...

each one having norm ≤ ||x||. Theorem. The Gelfand–Naimark representation of a C*-algebra is an isometric *-representation. It suffices to show the map...

In mathematics, the Riesz–Markov–Kakutani representation theorem relates linear functionals on spaces of continuous functions on a locally compact space...

In economics, a utility representation theorem shows that, under certain conditions, a preference ordering can be represented by a real-valued utility...

Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem is fundamental...

Galois representation Glossary of representation theory Group representation Itô's theorem List of representation theory topics List of harmonic analysis...

Zeilberger–Bressoud theorem (combinatorics) Birkhoff's representation theorem (lattice theory) Boolean prime ideal theorem (mathematical logic) Bourbaki–Witt theorem (order...

mathematics, Zeckendorf's theorem, named after Belgian amateur mathematician Edouard Zeckendorf, is a theorem about the representation of integers as sums of...

or the Wold representation theorem (not to be confused with the Wold theorem that is the discrete-time analog of the Wiener–Khinchin theorem), named after...

In economics, the Debreu's theorems are preference representation theorems—statements about the representation of a preference ordering by a real-valued...

the theorem. The method used to produce a ∗ {\displaystyle *} -representation from a state of A {\displaystyle A} in the proof of the above theorem is...

Weyl 1927). The theorem is a collection of results generalizing the significant facts about the decomposition of the regular representation of any finite...

infinite. In 1926, Frank Ramsey introduced Ramsey's Representation Theorem. This representation theorem for expected utility assumes that preferences are...

In mathematics and statistics, Skorokhod's representation theorem is a result that shows that a weakly convergent sequence of probability measures whose...

positive measure on the circle. This result, the Herglotz-Riesz representation theorem, was proved independently by Gustav Herglotz and Frigyes Riesz in...

In mathematics, the Borel–Weil–Bott theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can...

space Rising sun lemma Denjoy–Riesz theorem F. and M. Riesz theorem Riesz representation theorem Riesz-Fischer theorem Riesz groups Riesz's lemma Riesz projector...

his investigation of Boolean algebras, which culminated in his representation theorem for Boolean algebras. The following conditions on the topological...

established by Gustav Herglotz (see also the related Herglotz representation theorem.) Bochner's theorem for a locally compact abelian group G {\displaystyle G}...

matrices Birkhoff's HSP theorem, concerning the closure operations of homomorphism, subalgebra and product Birkhoff's representation theorem for distributive...

Kolmogorov–Arnold representation theorem is similar in spirit. Indeed, certain neural network families can directly apply the Kolmogorov–Arnold theorem to yield...

Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be...

Riesz representation theorem M. Riesz extension theorem Riesz–Thorin theorem Riesz–Fischer theorem Riesz's lemma Riesz–Markov–Kakutani representation theorem...